hw-11-11-taylor2 - Chapter 11.11 homework: Taylor and...

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Chapter 11.11 homework: Taylor and Maclaurin series Applications #1 #6 #31 Review problems (not optional, but the usual even/odd policy applies) #2 #3 #55 Question A: i) An Amtrak train is currently (time=0) at position 0, going 20 meters/sec, accelerating at 3 m/s^2. What will its position be after 2 seconds? ii) A train is going 15 meters/sec, accelerating at 3 m/s^2. How far will it go in 2 seconds? iii) A train is currently (time=0) at position 0, going 5 meters/sec, accelerating at 1.5 m/s^2, with a jerk of 0.55 m/s^3 and a snap of 0.01 m/s^4. What will its position be after 2 seconds? iv) Consider that same train from part (iii). What is its velocity at t=2? v) Consider that same train from part (iii). What is its acceleration at t=2? Question B: i) If you do a first-order Taylor approximation to sin(x) at x=pi/4, will your results be an upper bound or lower bound (or neither) on sin(x) for values of x close to pi/4 ? ii) If you do a 2nd-order Maclaurin approximation to cos(x),
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hw-11-11-taylor2 - Chapter 11.11 homework: Taylor and...

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